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Quantification of Active Product Ingredient in a Pharmaceutical

Raman Spectroscopy Data and Multivariate Curve Resolution with Alternating Least Squares (MCR-ALS)

Ricardo Cunha

27 October, 2024

Source: vignettes/articles/demo_paracetamol_quantification_mcrals.Rmd
demo_paracetamol_quantification_mcrals.Rmd



This article demonstrates how StreamFind can be used to quantity the active product ingredient (API) in Fizamol (i.e., paracetamol) from Raman data and using the Multivariate Curve Resolution with Alternating Least Squares (MCR-ALS) statistical method. A calibration curve is acquired with pure paracetamol diluted in water at different concentrations. Two Fizamol tablets (fiz_a and fiz_b) are diluted in water to a concentration of approx. 10 mg/ml and pure paracetamol (par) at 10 mg/ml are measured for quantification. Water is used as a blank.

# Creates the engine for Raman data
raman <- RamanEngine$new(analyses = raman_files)

# Modifies the replicate names
raman$analyses$replicates <- c(
  rep("blank", 9),
  rep("fiz_a", 9),
  rep("fiz_b", 9),
  rep("par", 3),
  rep("cali_150_mgml", 9),
  rep("cali_010_mgml", 9),
  rep("cali_025_mgml", 9),
  rep("cali_050_mgml", 9),
  rep("cali_075_mgml", 9)
)

# Modifies the blank names
raman$analyses$blanks <- c(rep("blank", length(raman$analyses)))



Overview of Raman analyses and respective analysis replicate groups and blanks.
analysis replicate blank concentration
240411_blank_200mW_OD3_2s_36n_pos1_r1 blank blank 0.0
240411_blank_200mW_OD3_2s_36n_pos1_r2 blank blank 0.0
240411_blank_200mW_OD3_2s_36n_pos1_r3 blank blank 0.0
240411_blank_200mW_OD3_2s_36n_pos2_r1 blank blank 0.0
240411_blank_200mW_OD3_2s_36n_pos2_r2 blank blank 0.0
240411_blank_200mW_OD3_2s_36n_pos2_r3 blank blank 0.0
240411_blank_200mW_OD3_2s_36n_pos3_r1 blank blank 0.0
240411_blank_200mW_OD3_2s_36n_pos3_r2 blank blank 0.0
240411_blank_200mW_OD3_2s_36n_pos3_r3 blank blank 0.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos1_r1 cali_010_mgml blank 1.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos1_r2 cali_010_mgml blank 1.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos1_r3 cali_010_mgml blank 1.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos2_r1 cali_010_mgml blank 1.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos2_r2 cali_010_mgml blank 1.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos2_r3 cali_010_mgml blank 1.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos3_r1 cali_010_mgml blank 1.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos3_r2 cali_010_mgml blank 1.0
240412_Paracetamol-1mgmL_200mW_OD3_2s_36n_pos3_r3 cali_010_mgml blank 1.0
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos1_r1 cali_025_mgml blank 2.5
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos1_r2 cali_025_mgml blank 2.5
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos1_r3 cali_025_mgml blank 2.5
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos2_r1 cali_025_mgml blank 2.5
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos2_r2 cali_025_mgml blank 2.5
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos2_r3 cali_025_mgml blank 2.5
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos3_r1 cali_025_mgml blank 2.5
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos3_r2 cali_025_mgml blank 2.5
240412_Paracetamol-2.5mgmL_200mW_OD3_2s_36n_pos3_r3 cali_025_mgml blank 2.5
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos1_r1 cali_050_mgml blank 5.0
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos1_r2 cali_050_mgml blank 5.0
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos1_r3 cali_050_mgml blank 5.0
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos2_r1 cali_050_mgml blank 5.0
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos2_r2 cali_050_mgml blank 5.0
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos2_r3 cali_050_mgml blank 5.0
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos3_r1 cali_050_mgml blank 5.0
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos3_r2 cali_050_mgml blank 5.0
240412_Paracetamol-5mgmL_200mW_OD3_2s_36n_pos3_r3 cali_050_mgml blank 5.0
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos1_r1 cali_075_mgml blank 7.5
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos1_r2 cali_075_mgml blank 7.5
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos1_r3 cali_075_mgml blank 7.5
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos2_r1 cali_075_mgml blank 7.5
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos2_r2 cali_075_mgml blank 7.5
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos2_r3 cali_075_mgml blank 7.5
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos3_r1 cali_075_mgml blank 7.5
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos3_r2 cali_075_mgml blank 7.5
240412_Paracetamol-7.5mgmL_200mW_OD3_2s_36n_pos3_r3 cali_075_mgml blank 7.5
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos1_r1 cali_150_mgml blank 15.0
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos1_r2 cali_150_mgml blank 15.0
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos1_r3 cali_150_mgml blank 15.0
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos2_r1 cali_150_mgml blank 15.0
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos2_r2 cali_150_mgml blank 15.0
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos2_r3 cali_150_mgml blank 15.0
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos3_r1 cali_150_mgml blank 15.0
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos3_r2 cali_150_mgml blank 15.0
240412_Paracetamol-15mgmL_200mW_OD3_2s_36n_pos3_r3 cali_150_mgml blank 15.0
240411_Fizamol-11_200mW_OD3_2s_36n_pos1_r1 fiz_a blank NA
240411_Fizamol-11_200mW_OD3_2s_36n_pos1_r2 fiz_a blank NA
240411_Fizamol-11_200mW_OD3_2s_36n_pos1_r3 fiz_a blank NA
240411_Fizamol-11_200mW_OD3_2s_36n_pos2_r1 fiz_a blank NA
240411_Fizamol-11_200mW_OD3_2s_36n_pos2_r2 fiz_a blank NA
240411_Fizamol-11_200mW_OD3_2s_36n_pos2_r3 fiz_a blank NA
240411_Fizamol-11_200mW_OD3_2s_36n_pos3_r1 fiz_a blank NA
240411_Fizamol-11_200mW_OD3_2s_36n_pos3_r2 fiz_a blank NA
240411_Fizamol-11_200mW_OD3_2s_36n_pos3_r3 fiz_a blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos1_r1 fiz_b blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos1_r2 fiz_b blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos1_r3 fiz_b blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos2_r1 fiz_b blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos2_r2 fiz_b blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos2_r3 fiz_b blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos3_r1 fiz_b blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos3_r2 fiz_b blank NA
240411_Fizamol-12_200mW_OD3_2s_36n_pos3_r3 fiz_b blank NA
240412_Paracetamol-10mgmL_200mW_OD3_2s_36n_pos3_r1 par blank NA
240412_Paracetamol-10mgmL_200mW_OD3_2s_36n_pos3_r2 par blank NA
240412_Paracetamol-10mgmL_200mW_OD3_2s_36n_pos3_r3 par blank NA 



raman$plot_spectra(colorBy = "replicates")

Raw Raman spectra for each analysis replicate.

Pre-processing Raman Data

The data is pre-processed using a workflow that includes the following steps:

  1. Averaging the spectra for each analysis replicate.
  2. Subtracting the blank spectra.
  3. Smoothing the spectra using the Savitzky-Golay method.
  4. Deleting the spectra sections that are not relevant for the analysis.
  5. Correcting the spectra baseline using the Asymmetric Least Squares (airPLS) method.

The methods ca be applied one at the time or used to bluid a Workflow object that will apply all methods in sequence within engine, as shown below.

# Creates the workflow for Raman data
# with an ordered list of processing settings
raman_workflow <- StreamFind::Workflow(
  list(
    RamanSettings_AverageSpectra_StreamFind(),
    RamanSettings_SubtractBlankSpectra_StreamFind(),
    RamanSettings_SmoothSpectra_savgol(fl = 21, forder = 4, dorder = 0),
    RamanSettings_DeleteSpectraSection_StreamFind(shiftmin = -100, shiftmax = 350),
    RamanSettings_DeleteSpectraSection_StreamFind(shiftmin = 1800, shiftmax = 2500),
    RamanSettings_CorrectSpectraBaseline_airpls(lambda = 45, differences = 1, itermax = 30)
  )
)

show(raman_workflow)

Workflow
 1: AverageSpectra (StreamFind)
 2: SubtractBlankSpectra (StreamFind)
 3: SmoothSpectra (savgol)
 4: DeleteSpectraSection (StreamFind)
 5: DeleteSpectraSection (StreamFind)
 6: CorrectSpectraBaseline (airpls)
# Adds the workflow to the engine
raman$workflow <- raman_workflow

# Runs the workflow
raman$run_workflow()
raman$plot_spectra()

Pre-processed Raman spectra for analysis replicate.

Applying MCR-ALS for Quantification

The quantification of paracetamol from the pre-processed Raman spectra is performed using the Multivariate Curve Resolution (MCR) with Alternating Least Squares (ALS) method via integration of the mdatools R package.

# Gets a matrix with spectra from the Raman engine
raman_matrix <- raman$get_spectra_matrix()
str(raman_matrix)
 num [1:8, 1:574] 221 304 384 714 183 ...
 - attr(*, "dimnames")=List of 2
  ..$ : chr [1:8] "fiz_a" "fiz_b" "par" "cali_150_mgml" ...
  ..$ : chr [1:574] "350.35779" "353.3808" "356.40076" "359.41766" ...
 - attr(*, "xValues")= num [1:574] 350 353 356 359 362 ...
# Creates the statistic engine for the statistic analysis
stat <- StatisticEngine$new(analyses = raman_matrix)

stat

StatisticEngine
name          NA
date          2024-10-27 13:04:44.891242
file          NA

Workflow empty 

StreamFind::StatisticAnalyses
         analysis  type features
 1: cali_010_mgml model      574
 2: cali_025_mgml model      574
 3: cali_050_mgml model      574
 4: cali_075_mgml model      574
 5: cali_150_mgml model      574
 6:         fiz_a model      574
 7:         fiz_b model      574
 8:           par model      574

Results empty 
# Applies the MCR-ALS method with the run method of the engine
stat$run(StatisticSettings_MakeModel_mcrals_mdatools(ncomp = 2))
plot(stat$model)

Overview plot for the MCR-ALS model 

# Applies the quantification method with the run method of the engine
# Concentrations with NA for unknown values
stat$run(
  StatisticSettings_Quantify_mcrals(
    concentrations = c(1, 2.5, 5.0, 7.5, 15.0, NA_real_, NA_real_, NA_real_)
  )
)

The MCR-ALS was applied with two components and the quantification results are shown below. The component with the highest combined explained variance and R2 values for the calibration curve should be used for quantification. The analysis par should have about 10 in mg/ml of paracetamol while the analyses fiz_a and fiz_b should a little less than 10 mg/ml due to presence of formulation ingredients and possible loss of API during sample preparation.

# Gets the quantification results
stat$quantification@quantities
$`Comp 1`
   result      analysis  intensity concentration  rsquared exp_variance
   <char>        <char>      <num>         <num>     <num>        <num>
1:  model cali_010_mgml    1.74826       1.00000 0.8204218         26.5
2:  model cali_025_mgml    0.00000       2.50000 0.8204218         26.5
3:  model cali_050_mgml    0.00000       5.00000 0.8204218         26.5
4:  model cali_075_mgml    5.15870       7.50000 0.8204218         26.5
5:  model cali_150_mgml   97.78008      15.00000 0.8204218         26.5
6:  model         fiz_a 2574.24296     302.32359 0.8204218         26.5
7:  model         fiz_b 2560.22155     300.69743 0.8204218         26.5
8:  model           par   83.92187      13.50472 0.8204218         26.5

$`Comp 2`
   result      analysis intensity concentration  rsquared exp_variance
   <char>        <char>     <num>         <num>     <num>        <num>
1:  model cali_010_mgml  113.9242      1.000000 0.9980675         73.3
2:  model cali_025_mgml  278.4266      2.500000 0.9980675         73.3
3:  model cali_050_mgml  615.1774      5.000000 0.9980675         73.3
4:  model cali_075_mgml  944.3979      7.500000 0.9980675         73.3
5:  model cali_150_mgml 2068.4674     15.000000 0.9980675         73.3
6:  model         fiz_a  914.8382      6.985566 0.9980675         73.3
7:  model         fiz_b  914.1857      6.980938 0.9980675         73.3
8:  model           par 1279.5648      9.572403 0.9980675         73.3